while our specific theories are becoming more numerous and more detailed, they are continually being ‘demoted’ as the understanding they contain is taken over by deep, general theories. And those theories are becoming fewer, deeper and more general. By ‘more general’ I mean that each of them says more, about a wider range of situations, than several distinct theories did previously. By ‘deeper’ I mean that each of them explains more – embodies more understanding – than its predecessors did, combined.
Also see Hardy’s mathematicians apology—his grasping at what it means for a problem to be important it has some depth. Here’s depth.
